integral of (x^2)/((x-3)^2)

Lösung

\int \frac{x ^{2}}{( x - 3 ) ^{2}} d x

- \frac{x ^{2}}{x - 3} + 2 (x - 3 + 3 ln ∣ x - 3 ∣) + C

Schritte zur Lösung

\int \frac{x ^{2}}{( x - 3 ) ^{2}} d x

Wende die partielle Integration an

= - \frac{x ^{2}}{x - 3} - \int - \frac{2 x}{x - 3} d x

\int - \frac{2 x}{x - 3} d x = - 2 (x - 3 + 3 ln ∣ x - 3 ∣)

= - \frac{x ^{2}}{x - 3} - (- 2 (x - 3 + 3 ln ∣ x - 3 ∣))

Vereinfache

= - \frac{x ^{2}}{x - 3} + 2 (x - 3 + 3 ln ∣ x - 3 ∣)

Füge eine Konstante zur Lösung hinzu

= - \frac{x ^{2}}{x - 3} + 2 (x - 3 + 3 ln ∣ x - 3 ∣) + C

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